YES Input TRS: 1: 2(5(x1)) -> 1(3(3(0(1(0(x1)))))) 2: 2(5(x1)) -> 2(2(0(5(0(1(x1)))))) 3: 3(5(x1)) -> 1(3(2(0(0(1(x1)))))) 4: 3(5(x1)) -> 3(2(0(5(3(0(x1)))))) 5: 4(5(x1)) -> 2(2(1(3(2(1(x1)))))) 6: 4(5(x1)) -> 3(2(0(5(0(0(x1)))))) 7: 1(2(5(x1))) -> 1(0(5(0(5(4(x1)))))) 8: 1(2(5(x1))) -> 1(2(2(1(0(1(x1)))))) 9: 1(2(5(x1))) -> 2(0(1(3(1(0(x1)))))) 10: 1(4(5(x1))) -> 1(2(4(0(2(1(x1)))))) 11: 2(5(1(x1))) -> 2(2(2(1(2(3(x1)))))) 12: 2(5(2(x1))) -> 4(0(2(2(3(3(x1)))))) 13: 2(5(3(x1))) -> 2(0(4(1(3(3(x1)))))) 14: 2(5(4(x1))) -> 2(0(5(1(0(1(x1)))))) 15: 3(2(5(x1))) -> 3(2(0(1(0(5(x1)))))) 16: 3(4(2(x1))) -> 3(4(0(2(2(2(x1)))))) 17: 3(5(1(x1))) -> 0(4(2(0(0(5(x1)))))) 18: 3(5(1(x1))) -> 0(4(2(2(3(4(x1)))))) 19: 3(5(1(x1))) -> 2(1(4(1(0(1(x1)))))) 20: 3(5(2(x1))) -> 0(4(3(2(2(2(x1)))))) 21: 3(5(2(x1))) -> 2(0(2(2(3(0(x1)))))) 22: 3(5(2(x1))) -> 2(3(3(2(1(2(x1)))))) 23: 3(5(3(x1))) -> 0(2(4(3(3(0(x1)))))) 24: 3(5(3(x1))) -> 0(5(4(3(3(0(x1)))))) 25: 3(5(3(x1))) -> 2(3(4(0(4(2(x1)))))) 26: 3(5(4(x1))) -> 0(2(0(5(0(0(x1)))))) 27: 3(5(4(x1))) -> 0(5(0(0(1(2(x1)))))) 28: 3(5(5(x1))) -> 0(5(4(1(0(5(x1)))))) 29: 4(5(1(x1))) -> 2(1(0(5(3(3(x1)))))) 30: 4(5(2(x1))) -> 0(5(1(0(0(4(x1)))))) 31: 4(5(4(x1))) -> 2(2(1(0(4(2(x1)))))) 32: 4(5(4(x1))) -> 3(2(0(3(2(0(x1)))))) 33: 5(5(3(x1))) -> 5(1(0(1(2(2(x1)))))) 34: 5(5(4(x1))) -> 5(1(0(4(2(2(x1)))))) Number of strict rules: 34 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #2(5(x1)) -> #2(2(0(5(0(1(x1)))))) #2: #2(5(x1)) -> #2(0(5(0(1(x1))))) #3: #2(5(x1)) -> #5(0(1(x1))) #4: #2(5(x1)) -> #1(x1) #5: #4(5(1(x1))) -> #2(1(0(5(3(3(x1)))))) #6: #4(5(1(x1))) -> #1(0(5(3(3(x1))))) #7: #4(5(1(x1))) -> #5(3(3(x1))) #8: #4(5(1(x1))) -> #3(3(x1)) #9: #4(5(1(x1))) -> #3(x1) #10: #4(5(x1)) -> #3(2(0(5(0(0(x1)))))) #11: #4(5(x1)) -> #2(0(5(0(0(x1))))) #12: #4(5(x1)) -> #5(0(0(x1))) #13: #2(5(3(x1))) -> #2(0(4(1(3(3(x1)))))) #14: #2(5(3(x1))) -> #4(1(3(3(x1)))) #15: #2(5(3(x1))) -> #1(3(3(x1))) #16: #2(5(3(x1))) -> #3(3(x1)) #17: #1(2(5(x1))) -> #2(0(1(3(1(0(x1)))))) #18: #1(2(5(x1))) -> #1(3(1(0(x1)))) #19: #1(2(5(x1))) -> #3(1(0(x1))) #20: #1(2(5(x1))) -> #1(0(x1)) #21: #2(5(1(x1))) -> #2(2(2(1(2(3(x1)))))) #22: #2(5(1(x1))) -> #2(2(1(2(3(x1))))) #23: #2(5(1(x1))) -> #2(1(2(3(x1)))) #24: #2(5(1(x1))) -> #1(2(3(x1))) #25: #2(5(1(x1))) -> #2(3(x1)) #26: #2(5(1(x1))) -> #3(x1) #27: #3(5(3(x1))) -> #5(4(3(3(0(x1))))) #28: #3(5(3(x1))) -> #4(3(3(0(x1)))) #29: #3(5(3(x1))) -> #3(3(0(x1))) #30: #3(5(3(x1))) -> #3(0(x1)) #31: #3(5(3(x1))) -> #2(4(3(3(0(x1))))) #32: #3(5(3(x1))) -> #4(3(3(0(x1)))) #33: #3(5(3(x1))) -> #3(3(0(x1))) #34: #3(5(3(x1))) -> #3(0(x1)) #35: #2(5(2(x1))) -> #4(0(2(2(3(3(x1)))))) #36: #2(5(2(x1))) -> #2(2(3(3(x1)))) #37: #2(5(2(x1))) -> #2(3(3(x1))) #38: #2(5(2(x1))) -> #3(3(x1)) #39: #2(5(2(x1))) -> #3(x1) #40: #4(5(4(x1))) -> #2(2(1(0(4(2(x1)))))) #41: #4(5(4(x1))) -> #2(1(0(4(2(x1))))) #42: #4(5(4(x1))) -> #1(0(4(2(x1)))) #43: #4(5(4(x1))) -> #4(2(x1)) #44: #4(5(4(x1))) -> #2(x1) #45: #2(5(4(x1))) -> #2(0(5(1(0(1(x1)))))) #46: #2(5(4(x1))) -> #5(1(0(1(x1)))) #47: #2(5(4(x1))) -> #1(0(1(x1))) #48: #2(5(4(x1))) -> #1(x1) #49: #4(5(2(x1))) -> #5(1(0(0(4(x1))))) #50: #4(5(2(x1))) -> #1(0(0(4(x1)))) #51: #4(5(2(x1))) -> #4(x1) #52: #3(5(3(x1))) -> #2(3(4(0(4(2(x1)))))) #53: #3(5(3(x1))) -> #3(4(0(4(2(x1))))) #54: #3(5(3(x1))) -> #4(0(4(2(x1)))) #55: #3(5(3(x1))) -> #4(2(x1)) #56: #3(5(3(x1))) -> #2(x1) #57: #3(5(2(x1))) -> #4(3(2(2(2(x1))))) #58: #3(5(2(x1))) -> #3(2(2(2(x1)))) #59: #3(5(2(x1))) -> #2(2(2(x1))) #60: #3(5(2(x1))) -> #2(2(x1)) #61: #1(2(5(x1))) -> #1(0(5(0(5(4(x1)))))) #62: #1(2(5(x1))) -> #5(0(5(4(x1)))) #63: #1(2(5(x1))) -> #5(4(x1)) #64: #1(2(5(x1))) -> #4(x1) #65: #1(4(5(x1))) -> #1(2(4(0(2(1(x1)))))) #66: #1(4(5(x1))) -> #2(4(0(2(1(x1))))) #67: #1(4(5(x1))) -> #4(0(2(1(x1)))) #68: #1(4(5(x1))) -> #2(1(x1)) #69: #1(4(5(x1))) -> #1(x1) #70: #5(5(3(x1))) -> #5(1(0(1(2(2(x1)))))) #71: #5(5(3(x1))) -> #1(0(1(2(2(x1))))) #72: #5(5(3(x1))) -> #1(2(2(x1))) #73: #5(5(3(x1))) -> #2(2(x1)) #74: #5(5(3(x1))) -> #2(x1) #75: #4(5(x1)) -> #2(2(1(3(2(1(x1)))))) #76: #4(5(x1)) -> #2(1(3(2(1(x1))))) #77: #4(5(x1)) -> #1(3(2(1(x1)))) #78: #4(5(x1)) -> #3(2(1(x1))) #79: #4(5(x1)) -> #2(1(x1)) #80: #4(5(x1)) -> #1(x1) #81: #3(5(5(x1))) -> #5(4(1(0(5(x1))))) #82: #3(5(5(x1))) -> #4(1(0(5(x1)))) #83: #3(5(5(x1))) -> #1(0(5(x1))) #84: #3(5(2(x1))) -> #2(3(3(2(1(2(x1)))))) #85: #3(5(2(x1))) -> #3(3(2(1(2(x1))))) #86: #3(5(2(x1))) -> #3(2(1(2(x1)))) #87: #3(5(2(x1))) -> #2(1(2(x1))) #88: #3(5(2(x1))) -> #1(2(x1)) #89: #5(5(4(x1))) -> #5(1(0(4(2(2(x1)))))) #90: #5(5(4(x1))) -> #1(0(4(2(2(x1))))) #91: #5(5(4(x1))) -> #4(2(2(x1))) #92: #5(5(4(x1))) -> #2(2(x1)) #93: #5(5(4(x1))) -> #2(x1) #94: #3(5(4(x1))) -> #5(0(0(1(2(x1))))) #95: #3(5(4(x1))) -> #1(2(x1)) #96: #3(5(4(x1))) -> #2(x1) #97: #3(5(1(x1))) -> #4(2(0(0(5(x1))))) #98: #3(5(1(x1))) -> #2(0(0(5(x1)))) #99: #3(5(1(x1))) -> #5(x1) #100: #4(5(4(x1))) -> #3(2(0(3(2(0(x1)))))) #101: #4(5(4(x1))) -> #2(0(3(2(0(x1))))) #102: #4(5(4(x1))) -> #3(2(0(x1))) #103: #4(5(4(x1))) -> #2(0(x1)) #104: #3(5(1(x1))) -> #2(1(4(1(0(1(x1)))))) #105: #3(5(1(x1))) -> #1(4(1(0(1(x1))))) #106: #3(5(1(x1))) -> #4(1(0(1(x1)))) #107: #3(5(1(x1))) -> #1(0(1(x1))) #108: #3(5(4(x1))) -> #2(0(5(0(0(x1))))) #109: #3(5(4(x1))) -> #5(0(0(x1))) #110: #3(5(2(x1))) -> #2(0(2(2(3(0(x1)))))) #111: #3(5(2(x1))) -> #2(2(3(0(x1)))) #112: #3(5(2(x1))) -> #2(3(0(x1))) #113: #3(5(2(x1))) -> #3(0(x1)) #114: #3(4(2(x1))) -> #3(4(0(2(2(2(x1)))))) #115: #3(4(2(x1))) -> #4(0(2(2(2(x1))))) #116: #3(4(2(x1))) -> #2(2(2(x1))) #117: #3(4(2(x1))) -> #2(2(x1)) #118: #3(5(x1)) -> #1(3(2(0(0(1(x1)))))) #119: #3(5(x1)) -> #3(2(0(0(1(x1))))) #120: #3(5(x1)) -> #2(0(0(1(x1)))) #121: #3(5(x1)) -> #1(x1) #122: #2(5(x1)) -> #1(3(3(0(1(0(x1)))))) #123: #2(5(x1)) -> #3(3(0(1(0(x1))))) #124: #2(5(x1)) -> #3(0(1(0(x1)))) #125: #2(5(x1)) -> #1(0(x1)) #126: #1(2(5(x1))) -> #1(2(2(1(0(1(x1)))))) #127: #1(2(5(x1))) -> #2(2(1(0(1(x1))))) #128: #1(2(5(x1))) -> #2(1(0(1(x1)))) #129: #1(2(5(x1))) -> #1(0(1(x1))) #130: #1(2(5(x1))) -> #1(x1) #131: #3(2(5(x1))) -> #3(2(0(1(0(5(x1)))))) #132: #3(2(5(x1))) -> #2(0(1(0(5(x1))))) #133: #3(2(5(x1))) -> #1(0(5(x1))) #134: #3(5(x1)) -> #3(2(0(5(3(0(x1)))))) #135: #3(5(x1)) -> #2(0(5(3(0(x1))))) #136: #3(5(x1)) -> #5(3(0(x1))) #137: #3(5(x1)) -> #3(0(x1)) #138: #3(5(1(x1))) -> #4(2(2(3(4(x1))))) #139: #3(5(1(x1))) -> #2(2(3(4(x1)))) #140: #3(5(1(x1))) -> #2(3(4(x1))) #141: #3(5(1(x1))) -> #3(4(x1)) #142: #3(5(1(x1))) -> #4(x1) Number of SCCs: 1, DPs: 20 SCC { #4 #9 #26 #39 #44 #48 #51 #56 #64 #69 #74 #80 #88 #93 #95 #96 #99 #121 #130 #142 } POLO(Sum)... succeeded. 1 w: x1 + 24870 4 w: x1 + 1 5 w: x1 + 99477 3 w: x1 + 24867 #2 w: x1 #4 w: x1 + 149215 0 w: 24870 #3 w: x1 + 24869 #5 w: x1 2 w: x1 + 24870 #1 w: x1 + 99476 USABLE RULES: { 1..4 7..28 } Removed DPs: #4 #9 #26 #39 #44 #48 #51 #56 #64 #69 #74 #80 #88 #93 #95 #96 #99 #121 #130 #142 Number of SCCs: 0, DPs: 0